ANALYTICAL MECHANICS INTRODUCTION. 1. Scope and Aim of Mechanics.-—Mechanics is the science of motion. It has a twofold object: First, to describe the motions of bodies and to interpret them by means of a few laws and principles, which are generalizations derived from observation and experience. Second, to predict the motion of bodies for all times when the circumstances of the motion for any one instant are given, in addition to the special laws which govern the motion. The present tendency in science is toward regarding all physical phenomena as manifestations of motion. Complicated and apparently dissimilar phenomena are being explained by the interactions and motions of electrons, atoms, molecules, colls, and other particles. The kinetic theory of heat, the wave theories of sound and light, and the electron theory of electricity are examples which illustrate the tendency toward a mechanical interpretation of the physical universe. This tendency not only emphasizes the fundamental importance of the science of mechanics to other physical sciences and engineering but it also broadens the aim of the science and makes the dynamical interpretation of all physical phenomena its ultimate object. The aim of elementary mechanics is, however, very modest and its scope is limited to the discussion of the simplest cases of motion and equilibrium which occur in nature.